Applied Mathematics, University of Waterloo
Higher dimensional slow manifolds in chemical reaction networks
In the context of geometric methods for enzyme kinetics, the steady state (SSA) and rapid equilibrium (EA) approximations correspond to surfaces in the phase space. A description of a so called trapping region $\Gamma$ is given in terms of such surfaces. Conditions for uniqueness and existence of an invariant manifold fully contained in $\Gamma$ are discussed. We will fully discuss the case when we have a two-dimensional system. At the end we present a possible path to follow to generalize these ideas to systems in higher dimensions.